The challenge of balancing individual cells connected in series is a well-known issue in the battery industry. Cells connected in series to form a battery system, even if they were “ideally” manufactured and identically characterized, over time will exhibit deviating electrochemical behavior. These behavioral differences are due, among other reasons, to manufacturing tolerances that get accented over time, but also due to differences in the environment within which each individual cell operates.
There are two major concerns regarding cell imbalance. The first one regards maximizing the charge a battery system can accept. The goal is to achieve 100% SOC for the whole battery system. The second concern regards the ability of the battery to provide the maximum amount of stored charge to the user. In an optimal situation the battery shuts down with minimum residual capacity having provided the maximum amount of its stored energy to the task at hand.
Achieving 100% SOC
In a battery consisting of N number of cells the overall battery SOCB can be expressed as the sum of the SOCn of each cell.
                              SOC          B                =                              1            N                    ⁢                                    ∑                              n                =                1                            N                        ⁢                                                  ⁢                          SOC              n                                                          (        1        )            
Since SOC is closely related to EMF (Electro Motive Force), it is obvious that in order to maximize the SOC of the whole pack, the open circuit voltage Voc of each cell after charging should be at the maximum value allowed by the chemistry and dictated by the operating guidelines of the cell manufacturer. In specific cell chemistries, like Lithium Ion, the charging process is terminated whenever any cell reaches its manufacturer defined maximum voltage. The maximum voltage is set at a value that ensures the battery safety and long term health.
Cells connected in series receive the same amount of charging current. Due to differences in their internal impedance, the cell with the highest impedance will reach the cutoff voltage earlier than other cells, forcing the control electronics to halt the charging process. As a result specific cells may not reach their optimum State of Charge (SOC) and the battery will not perform at its maximum potential. The percentage of SOC that the battery system achieves will depend on the value of the internal impedance, the charging method (pulse, DC, etc.) and the value of the charging current, among other factors.
FIG. 1 shows the equivalent circuit of a battery cell being charged with a slowly changing current. The voltage as measured at the cell terminals Vcell=Voc+IchgRs. The Rs value depends among other things on manufacturing variances, aging and cycle history, present SOC and temperature.
Several methods have been proposed to address this challenge. The most commonly used method in the industry today “bleeds” the cell whose Vcell value has reached the VMAX value and repeats the process of charging until all cells have reached the VMAX value. The shortcomings of this method are well known and have been referenced in several patents, such as U.S. Pat. No. 5,710,504 “Switched Capacitor System for automatic Battery Equalization” and U.S. Pat. No. 6,518,725 “Charge balancing system”. Published Japanese patent application 09-084275 “Method and Apparatus for Controlling Charging of Assembly Battery Pack” introduces a bypass mechanism combined with current reduction at the end of charge in order to avoid overheating cells, with the drawback of prolonged charge time. Sendyne's own U.S. Pat. No. 7,936,150 entitled “Cell protection and conditioning circuit and system” addresses also this same issue proposing a conditioning circuit that takes over charging of individual cells when their Vcell value starts approaching their VMAX.
Delivering the Stored Charge to the Load
Assuming the battery has been charged optimally, the next and probably most important performance issue is its ability to deliver the stored energy to the active load. If the load is constant or the variation is slow the equivalent circuit looks like the one used for charging with the only difference being the direction of the current.
The voltage in this case as measured at the cell terminals would be:Vcell=Voc−IdchgRs orVcell=EMF−IdchgRs  (2)
As can be seen in the above equation, cells with the same EMF connected in series can exhibit different terminal voltages Vcell depending on the value of their respective internal resistance.
If the load is changing dynamically as in the case of electric vehicles, instead of the internal resistance we can use the internal impedance Z in a similar relationship:Vcell=Voc−idchgZs  (3)
The cell impedance among other factors depends on the frequency content of the load current. A Nyquist representation of the frequency dependence for Lead Acid and LiIon cells is shown in FIGS. 3 and 4.
The high frequency portion on the left side of FIG. 4 is attributed to conductance of wires, connections, etc., the mid-section semi-circle to charge transfer and the electrochemical double layer, and in general the kinetics of the electrochemical cell reactions. The straight line segment on the right is attributed to limitations in mass charge transfer, also referred to as the diffusion limited part.
It can be appreciated that a dynamic load applied to a battery system will employ, to a different extent, all mechanisms of charge transfer. As a result, cell impedances and resulting cell terminal voltages will vary according to the frequency content of the load current.
The impedance Nyquist plot for each cell varies according to its SOC, temperature, aging and cycle history but also due to manufacturing variances as it is shown on the following figures.
The practical implication is that even if cells participating in a battery system, start with the same SOC and are operating at exactly the same conditions they will still exhibit differences in their internal impedances and the resulting terminal voltages due to manufacturing variances. Because the impedance differences are frequency dependent, the voltage differences among cells will depend on the load current frequencies. As a result, during discharge of a cell array, cells with the highest composite impedance at the specific load frequency spectrum, will reach the cell cutoff voltage first, even if their SOC is not the smallest one in the array.
The alert reader will appreciate that in order to prolong the battery operation, charge should not be distributed equally to every cell as it is the common concept and practice today, but it should be distributed in a manner that boosts the cells with the highest exhibited internal impedance based on the actual load frequency content. So practically in order to prolong battery life cell charge should be actively unbalanced.
Saying the same thing in a different way, while many investigators have expended much energy and ingenuity to attempting to make the charge of each cell as close as possible to being identical to each of the other cells, the invention as will be discussed below actually pursues the very different end of unbalanced cell charge among cells.
A Typical Cell Array
FIG. 6 shows part of a typical battery cell array.
In a typical implementation N-number of cells (2) is connected in series to form a cell-array. The array (1) can form the whole or part of a battery system. The voltage of each cell is monitored typically by a Cell Voltage Monitor circuit (3). Individual cells may have their own voltage monitoring device, or they can time-share one. Among other functions, the “Cell Voltage Monitor” device compares the cell voltage with a set of fixed values specific to the type of cell, a maximum voltage value VOVC (overcharge voltage) and a minimum VUNC (undercharge voltage) value. A control unit (4) controls a set of switches (5) that will selectively open if any of the cell voltages exceeds the VOVC value or becomes lower than the VUNC value. The set of switches is designed in such a way so they will prevent discharging but allow charging if the undercharge voltage is detected and they will prevent further charging while allowing discharging if the overvoltage is detected. The set of protection switches (5) may be one for the whole array as shown in FIG. 6, or one per cell if every cell employs its own protection circuit.
The Issue of Unbalanced Cells and Prior Art
It is appreciated that the first cell whose terminal voltage is detected to reach the VUNC (undercharge voltage) value will force the Control Unit (4) to open the protection switch (5) forcing the cell array to cease providing charge to the load. The cutoff value VUNC is provided by the cell manufacturer and adherence to guarantees that no irreversible damage will occur to the cell, due to super-saturation of the cathode or for other reasons. It is common knowledge in the industry that due to electrochemical differences among the cells, it is likely that not all the cells will reach simultaneously the VUNC (undercharge voltage) value. So when a cell reaches this value, the rest of the cells in the battery array may still have residual charge that is remaining unused. In order to avoid this situation, battery manufacturer employ different methods, such as:                Cell matching. Cells are measured during manufacturing and they are grouped according to their electrical characteristics which may include capacity, internal impedance, etc. so they will exhibit similar behavior under the same load        The thermal environment is controlled so all cells in the cell array, operate under the same temperature        Cells are “actively balanced”, usually during periods of inactivity in order to match their EMF. The goal of balancing is to equate the SOC of all the cells participating in the array, so they hold the same amount of charge.        Batteries are used along with super-capacitors that isolate the load variations from the battery cells.The Role of Cell Impedance in Battery Pack Performance        
When a battery is connected to a dynamic load, such as the load of an electric car, individual cells connected in series within the battery, will exhibit differences in their terminal voltage Vn, which is caused by two factors, as it is shown in the following equations:                The difference in their EMF        The difference in their impedance under the specific loadV1=EMF1+ILOAD*Z1 V2=(EMF1±ΔEMF)+ILOAD*(Z1±ΔZ)  (4)OrV2−V1=±ΔEMF±ILOAD*ΔZ  (5)        
From (5) it may be seen that the difference in terminal voltage between two cells depends not only on differences of their respective EMF, but also on the ILOAD current value and the dynamic difference of their internal impedance ΔZ. From (5) it can be appreciated that even if ΔEMF=0, which means the cells are “balanced” (in the traditional sense of the term), they will still exhibit dynamic voltage difference that depending on the current value, and the load, among other things, may cause the cell with the highest impedance to reach first the voltage cutoff value VUNC.